Characteristics of Instantaneous Secondary Flows

Secondary flows induced by spanwise-heterogeneous surface roughness significantly influence surface drag, convective heat transfer, and the transport of airborne scalars. While time-averaged fields for cases with large spanwise heterogeneity display domain-scale secondary flows, recent studies suggest these are artifacts of time-averaging, obscuring a highly transient flow field beneath. The prevailing understanding attributes the mean secondary flow structures to the ensemble imprint of compact, counter-rotating vortex pairs that appear in the instantaneous flow. However, how these structures reorganize to yield different mean polarities remains unclear. In this presentation, we examine the instantaneous dynamics of secondary flows across configurations with varying polarity. We show that regions of high- and low-momentum fluid do not remain fixed relative to either the roughness elements or the valleys between them, but instead switch in a chaotic, non-periodic manner. We further demonstrate that the vertical velocity signal exhibits low-frequency modulations with multi-modal probability distributions, highlighting that temporal variability in vertical momentum transport is a fundamental feature of secondary flow dynamics. Together, these findings offer new insight into how the geometric arrangement of roughness elements governs the unsteady behavior of secondary flows.